# Markov Volatility Random Walks

Markov Volatility Random Walks

A decent first approximation of real market price activity is a lognormal random walk. But with a fixed volatility parameter, such models miss several stylized facts about real financial markets. Allowing the volatility to change through time according to a simple Markov chain provides a much closer approximation to real markets. Here the Markov chain has just two possible states: normal or elevated volatility. Either state tends to persist, with a small chance of transitioning to the opposite state at each time-step.